Q. The resultant of two forces, each $P$, acting at an angle $\theta$ is
A) $2P\ $sin $\frac{\theta}{2}$
B) $2P\ $cos $\frac{\theta}{2}$
C) $2P\ $cos$\theta$
D) $P\sqrt{2}$
Explanation
(b) $R^{2} = P^{2} + P^{2} + 2P^{2}\ cos\theta$ or $R^{2} = 2P^{2} + 2P^{2}\ cos\theta$
or $R^{2} = 2P^{2}(1 + \ cos\theta)$
or $R^{2} = 2P^{2}\left( 1 + 2\cos^{2}{\frac{\theta}{2} - 1} \right)$
or $R^{2} = 4P^{2}\cos^{2}\frac{\theta}{2}$
or $R = 2P\cos^{\ }\frac{\theta}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.